

A161903


Convert n into a sequence of binary digits, apply one step of the rule 110 cellular automaton, and interpret the results as a binary integer.


5



0, 3, 6, 7, 12, 15, 14, 13, 24, 27, 30, 31, 28, 31, 26, 25, 48, 51, 54, 55, 60, 63, 62, 61, 56, 59, 62, 63, 52, 55, 50, 49, 96, 99, 102, 103, 108, 111, 110, 109, 120, 123, 126, 127, 124, 127, 122, 121, 112, 115, 118, 119, 124, 127, 126, 125, 104, 107, 110, 111, 100, 103, 98, 97, 192, 195, 198, 199, 204, 207, 206, 205, 216, 219, 222, 223, 220, 223, 218, 217, 240, 243, 246, 247, 252, 255, 254, 253, 248, 251, 254, 255, 244, 247, 242, 241, 224, 227, 230, 231, 236
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,2


COMMENTS

a(a(a(...1))) (n times) gives A006978(n)


LINKS

T. D. Noe, Table of n, a(n) for n = 0..1023
Index entries for sequences related to cellular automata
Eric Weisstein's World of Mathematics, Rule 110
Wikipedia, Rule 110


FORMULA

a(n) = A057889(A269174(A057889(n))).  Antti Karttunen, Jun 02 2018


EXAMPLE

For n=19, the evolution after one step is
0, 1, 0, 0, 1, 1 (n=19)
1, 1, 0, 1, 1, 1 (a(n)=55)
So a(n)=55.


MATHEMATICA

a[n_] :=
FromDigits[
Drop[Part[CellularAutomaton[110, {IntegerDigits[n, 2], 0}], 1], 1],
2]; Table[a[n], {n, 0, 100}]


CROSSREFS

Cf. A006978, A070887, A071049, A180001, A186083, A204371.
Cf. also A269160, A269174, A269175.
Sequence in context: A242666 A226228 A269174 * A163617 A189634 A047705
Adjacent sequences: A161900 A161901 A161902 * A161904 A161905 A161906


KEYWORD

nonn,base


AUTHOR

Ben Branman, Jan 30 2011


STATUS

approved



